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Math 2250 Week 3 Quiz Name, UID, and section TA: Write your answer in the space provided. Show work for full credit. There is a third problem on the back of this page. 1. (3 points) Consider the following differential equation for x(t), which could be modeling a logistic differential equation with harvesting x0 (t) = −x2 + 3x − 2. Find the equilibrium solutions. Then draw the phase diagram and indicate the stability for each equilibrium solution. 2. (3 points) Compute the partial fractions decomposition for 1 . (x − 1)(x − 2) 3. (4 points) Use your work from (2) to solve the initial value problem x0 (t) = −x2 + 3x − 2 x(0) = 3 Page 2